Efficiency Equation: How to Calculate It

This calculator works out the efficiency of any system that takes an energy input and delivers a useful output. You enter the useful output energy (or work) and the total input energy, and you get back the efficiency as a percentage. The same formula applies to engines, power plants, appliances, and biological processes.

Formula

The efficiency equation is:

Efficiency (η) = (Useful output energy / Total input energy) × 100%

In symbols: η = (E_out / E_in) × 100%

• η (eta) – efficiency, expressed as a percentage (%).
• E_out – useful energy or work delivered by the system, in joules (J) or any consistent energy unit.
• E_in – total energy supplied to the system, in the same unit as E_out.

The result is always between 0% and 100% for real systems. A value above 100% would mean you get more energy out than you put in, which violates the conservation of energy. (Heat pumps and refrigerators are described by a different metric, the coefficient of performance, because they move heat rather than convert it.)

Worked Example

Using the default values from the calculator: a motor receives 600 J of electrical energy and delivers 450 J of mechanical work.

1. Write down the formula: η = (E_out / E_in) × 100%
2. Plug in the numbers: η = (450 J / 600 J) × 100%
3. Divide: 450 / 600 = 0.75
4. Multiply by 100: 0.75 × 100 = 75%

The motor is 75% efficient. The remaining 150 J (600 – 450) is lost, mostly as heat and sound. The calculator shows this as the “Energy lost” output.

When to Use This Equation

The efficiency equation is used whenever you want to know how well a device or process converts input energy into the desired output. Common applications include:

• Electric motors – compare the electrical energy consumed with the mechanical work produced.
• Light bulbs – useful light output versus total electrical input (a traditional incandescent bulb is about 5% efficient; an LED can be over 30%).
• Power plants – chemical or nuclear energy in, electrical energy out. Typical coal plants are around 33–40% efficient.
• Human body – chemical energy from food versus mechanical work done; muscles are roughly 20–25% efficient.
• Appliances – water heaters, air conditioners, and refrigerators all have efficiency ratings.

In every case, you must clearly define what counts as “useful” output. For a car engine, useful output is the work delivered to the wheels, not the heat rejected through the exhaust and radiator.

How to Read the Result

A higher percentage means less energy is wasted. However, efficiency alone doesn’t tell you the whole story. A 95% efficient motor that is rarely used may waste more energy in a year than a 90% efficient motor that runs constantly. You also need to consider the total energy input and the operating time.

Efficiency is a ratio, so it has no units – the percentage sign just scales the decimal. If both energies are measured in the same unit (joules, kilowatt-hours, calories, etc.), the units cancel. You can use any energy unit as long as E_out and E_in are the same.

Common Mistakes and Misconceptions

• Mixing units – using joules for input and kilowatt-hours for output will give a wrong result. Convert everything to the same unit first.
• Confusing power with energy – efficiency is about energy (J) or work, not power (W). Power is energy per time. If you have power values, multiply by time to get energy before applying the formula.
• Using the wrong output – only the useful output counts. Heat from an electric heater is useful if you want heat, but it’s wasted if you want light.
• Thinking 100% is possible – every real process has some loss, usually as heat due to friction or resistance. The second law of thermodynamics prevents perfect efficiency.
• Ignoring the time factor – a device that is efficient but operates for a long time can still consume more energy than a less efficient one used briefly.

Limits of the Formula

This simple ratio works for steady-state systems where you can measure the total input and output energies. It does not capture:

• Time-varying behaviour – during startup, a motor may draw more power and be less efficient.
• Part-load efficiency – many devices are most efficient at full load, but operate at part load most of the time.
• Quality of energy – the formula treats all joules equally, but 1 J of electricity is more “valuable” than 1 J of low-temperature heat. Exergy analysis addresses this.
• Economic or environmental factors – efficiency doesn’t include cost, emissions, or resource availability. A highly efficient system may be too expensive to build or use rare materials.

For heat engines specifically, the Carnot efficiency gives the theoretical maximum based on the hot and cold reservoir temperatures. The simple formula here measures actual performance, not the theoretical limit.

Frequently Asked Questions

What is the difference between efficiency and effectiveness?

Efficiency is a ratio of useful output to total input – it measures how well resources are used. Effectiveness measures whether the goal is achieved at all, regardless of resource use. A machine can be effective (it does the job) but inefficient (it wastes a lot of energy), or efficient but ineffective (it does the wrong job well).

Can efficiency be over 100%?

No, not for the energy conversion described here. That would violate conservation of energy. However, devices like heat pumps have a coefficient of performance (COP) greater than 1 because they move heat from outside to inside using a small amount of electrical energy – they don’t convert electricity directly into heat, they transport it.

How do I calculate efficiency if I only have power ratings?

Multiply power by time to get energy. For example, if a device uses 100 W for 2 hours, the input energy is 100 W × 2 h = 200 Wh (or 0.2 kWh). Do the same for the useful output, then apply the formula. Ensure both energies are in the same unit.

Why is my calculated efficiency lower than the manufacturer’s rating?

Manufacturer ratings often use ideal conditions: steady load, correct voltage, optimal temperature. Real-world operation includes start-up losses, partial loads, voltage fluctuations, and aging components. Also, the rating may be based on a specific definition of “useful output” that differs from yours.

What is the efficiency of a typical car engine?

Modern gasoline engines are about 20–30% efficient at converting the chemical energy in fuel into mechanical work at the wheels. Diesel engines are slightly higher, around 30–40%. The rest is lost as heat in the exhaust and coolant, plus friction and pumping losses. Electric vehicles are much more efficient – around 85–90% from battery to wheels.

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in e_out | Useful output energy | J | 450 | 0
in e_in | Total input energy | J | 600 | 0
out eff | Efficiency | % | (e_out / e_in) * 100 | 1
out loss | Energy lost | J | e_in - e_out | 0